A solid immersion lens (SIL) is a refractive or diffractive, optical element that can be formed on or otherwise affixed to a substrate. Typically, a SIL is part of an objective lens that is brought into adjacent contact with the optical medium through which it is desirable to view an embedded object. A refractive SIL increases the magnification and the resolution of an object buried in the optical medium by modifying refraction as the light passes from the optical medium into air. SILs are becoming commercially available on advanced imaging systems capable of observing buried features with light that penetrates or emits from the medium. A flip-chip application specific integrated circuit (ASIC) fabricated on silicon (Si) is an exemplary candidate for a SIL since light longer than the wavelength of the optical band gap of silicon can easily transmit through the backside silicon of the flip-chip, reflecting off the circuitry beneath to provide an image of the circuitry for diagnostic purposes.
FIGS. 1A and 1B are prior art schematic diagrams illustrating the effect of a refractive SIL when viewing circuitry through an optical medium, such as silicon (Si). FIG. 1A shows circuitry 11 formed in silicon 12, which is referred to as “backside silicon” because it extends generally away from the plane on which the circuitry 11 is located. FIG. 1A shows the optical path used to view circuitry 11 on a flip-chip ASIC without a SIL. Light of wavelength longer than the energy band gap of silicon passes through the backside Si 12 and then continues to an objective lens of a microscope, also referred to as a “backing objective” 14. Without a SIL, light refracts as it crosses the boundary between the backside Si 12 and the air 16. This boundary point is shown using reference numeral 21. Light passing through the backside Si 12, shown as light ray 22, forms an angle “θ” with respect to an optical axis 24, which extends normal to the plane 26 on which the circuitry 11 is located. As the light refracts at the boundary point 21, light ray 28 forms an angle “φ” with respect to the optical axis 24, where the angle “θ” is less than the angle “φ” according to Snell's law.
FIG. 1B illustrates a sectional prior art illustration of a SIL 30. The SIL 30 is a section of a sphere made from Si and held in intimate contact with the surface 31 of the backside Si 12. In this example, the radius “r” of the SIL 30 is 1.5 mm, and the thickness of the backside Si is approximately 780 μm. The exposed portion 33 of the SIL 30 and the backside Si enclosed in the dashed arc 34 forms a hemisphere. With this geometry, the plane 26 of the circuitry 11 bisects a sphere where the Si hemisphere that forms the SIL 30 is used to direct the light. All light from the center of the sphere crosses the boundary 35 between the backside Si 12 and the SIL 30 without refraction if the SIL 30 and the backside Si 12 are in adjacent contact. Light passing through the backside Si 12, shown as light ray 36, forms an angle “φ” with respect to the optical axis 24. When a SIL 30 is implemented, all light 36 from the center of the sphere crosses the boundary 35 between the backside Si 12 and the SIL 30 without refraction, as shown at points 37, and maintains the constant angle “φ” with respect to the optical axis 24. The light rays 36 then cross the boundary 38 between the SIL 30 and air 16 normal to the boundary 38, exiting the SIL 30 without refraction.
The increase in the effective numerical aperture (NA, defined as sin(θ) in FIG. 1A and sin(φ) in FIG. 1B) for the SIL 30 is a key to the improvement in resolution when viewing the circuitry 11. The resolution of the optical system defined by FIG. 1A is the Raleigh condition:R=λSi/(2*NAθ),
where λSi and NAθ are the wavelength and numerical aperture of the light in the Si, respectively. Relative to their values in air, the wavelength of light in Si is λ/n where n=3.5 is the index of refraction of Si near-IR wavelengths (1.1 μm to 1.7 μm), and NA is governed by Snell's law n*sin(θ)=sin(φ) with φ being the angle of the light after refraction.
In FIG. 1B the surface of the Si is reshaped to be hemispherical to prevent refraction. Since all light rays in FIG. 1B strike the Si/air surface perpendicularly, refraction vanishes and the resolution becomes:RSIL=λSi/(2*NAφ),
where Snell's law no longer affects NA. The net effect of the hemispherical surface is to improve the resolution defined by the Raleigh condition according to the relationship:RSIL=R/n, and to improve the magnification by a factor of n.
The configuration of the SIL 30 is called a centric SIL because the object (portions of the circuitry 11 that are at a focal area of the SIL 30) is physically at the center of the hemisphere. In practice, the SIL 30 does not require the exact geometry shown because the backing objective 14 can move in the vertical dimension to compensate although the resolution and magnification will be affected.
A SIL is commercially available as a separate structure, or can be commercially formed on a surface of an optical medium using a focused ion beam (FIB) projected through a gray scale rendering of a milling pattern. A focused ion beam (FIB) uses a beam of Ga+ ions to strike and mechanically erode a surface of an optical medium. The length of time the Ga+ beam dwells at a point determines the depth of the mill. A prior technique can be used to form a hemispherical surface in an optical medium by projecting the hemispherical shape into a two-dimensional gray scale image where darker gray scale levels correspond to deeper milling. The gray scale then determines the dwell time, i.e. the length of time the FIB mills at each point. FIG. 2 is a diagram illustrating a two-dimensional gray-scale rendering 50 of a three-dimensional hemisphere. The two-dimensional gray-scale rendering 50 can be used to create a milling pattern to form the SIL 30. Such a SIL is formed as a hemispherical structure directly on the optical medium.
Unfortunately, many FIB milling tools cannot use a two-dimensional gray-scale rendering to control the milling performed by the FIB. Therefore, it would be desirable to have an alternative way of forming a high quality SIL on an optical medium.